Orifice Flow Rate Calculator
Compute the volumetric flow rate of a liquid discharging through a circular orifice under a given hydraulic head. Ideal for hydraulic engineers sizing outlet structures, tanks, and culverts.
About this calculator
Flow through an orifice is governed by Torricelli's theorem combined with the orifice area. The formula used here is: Q = Cd × (π × d² / 4) × √(2 × g × h), where Cd is the discharge coefficient (typically 0.61 for a sharp-edged orifice), d is the orifice diameter in metres, g = 9.81 m/s² is gravitational acceleration, and h is the hydraulic head in metres above the orifice centre. The square-root relationship between head and flow rate means that doubling the head increases flow by only about 41%. The discharge coefficient captures contraction of the jet (vena contracta) and frictional losses, and varies with orifice geometry and Reynolds number.
How to use
Suppose a sharp-edged orifice has a diameter of 0.08 m, a hydraulic head of 3 m, and a discharge coefficient of 0.61. Step 1 — orifice area factor: π × (0.08)² / 4 = 0.005027 m². Step 2 — velocity term: √(2 × 9.81 × 3) = √58.86 = 7.672 m/s. Step 3 — apply coefficient: Q = 0.61 × 0.005027 × 7.672 ≈ 0.02352 m³/s (about 23.5 litres per second). Increasing the head to 12 m would double the flow rate to roughly 47 litres per second.
Frequently asked questions
What discharge coefficient should I use for a sharp-edged orifice flow calculation?
For a standard sharp-edged circular orifice discharging freely into air or a downstream channel, a Cd of 0.61 is the widely accepted default derived from extensive experimental data. This value accounts for the vena contracta — the narrowing of the jet just downstream of the orifice — and frictional losses at the edge. Rounded or chamfered orifice edges allow the flow to follow the wall more smoothly, reducing contraction and raising Cd to around 0.80–0.98. Always use the manufacturer's or experimental value when precision matters, as Cd can also vary slightly with Reynolds number at very low flow velocities.
How does hydraulic head affect the flow rate through an orifice opening?
Hydraulic head (h) appears inside a square root in the orifice equation, so the relationship between head and flow is non-linear. Quadrupling the head only doubles the flow rate, not quadruples it. This diminishing return is important when designing overflow or drainage structures: adding more head provides progressively smaller gains in discharge capacity. Engineers use this relationship to size orifices that limit peak outflow from detention basins, ensuring downstream channels are not overwhelmed during storm events.
Why is an orifice flow rate calculator useful for stormwater detention pond design?
Detention ponds are often fitted with a low-level orifice outlet that controls the rate at which stored water is released after a storm, preventing downstream flooding. By knowing the required peak outflow and available head, an engineer can rearrange the orifice equation to solve for the needed orifice diameter. The calculator makes it easy to iterate — trying different diameters or coefficients — until the design outflow matches regulatory targets. It also allows verification that a proposed orifice will pass the full design storm volume within the required drawdown period.